Minimal non-contingency logic. (English) Zbl 0833.03005

Kuhn, Steven T.

Notre Dame J. Formal Logic 36, No. 2, 230-234 (1995).

Summary: Simple finite axiomatizations are given for versions of the modal logics \({\mathbf K}\) and \({\mathbf K} \mathbf{4}\) with non-contingency (or contingency) as the sole modal primitive. This answers two questions of I. L. Humberstone [posed in the paper reviewed above].

MSC:

03B45

Modal logic (including the logic of norms)

Keywords:

finite axiomatizations; modal logics; non-contingency

References:

[1]	Brogan, A. P., “Aristotle’s logic of statements about contingency,” Mind , vol. 76 (1967), pp. 49–81.
[2]	Cresswell, M. J., “Necessity and contingency,” Studia Logica , vol. 47 (1988), pp. 145–149. · Zbl 0666.03015 · doi:10.1007/BF00370288
[3]	Humberstone, I. L., “The logic of non-contingency,” Notre Dame Journal of Formal Logic , vol. 36 (1995), pp. 214–229. · Zbl 0833.03004 · doi:10.1305/ndjfl/1040248455
[4]	Mortensen, C., “A sequence of normal modal systems with non-contingency bases,” Logique et Analyse , vol. 19 (1976), pp. 341–344. · Zbl 0347.02014
[5]	Montgomery, H., and R. Routley, “Contingency and non-contingency bases for normal modal logics,” Logique et Analyse , vol. 9 (1966), pp. 318–328. · Zbl 0294.02008
[6]	Montgomery, H., and R. Routley, “Non-contingency axioms for S4 and S5 ,” Logique et Analyse , vol. 9 (1968), pp. 422–428. · Zbl 0169.30003
[7]	Montgomery, H., and R. Routley, “Modalities in a sequence of normal non-contingency modal systems,” Logique et Analyse , vol. 12 (1969), pp. 225–227. · Zbl 0196.00902